NCERT Chapter Mapping
The Universal Truth
Every chapter in mechanics uses FBD. Master it once — use it everywhere, forever.
Laws of Motion ⭐
Core concept. Newton's laws, normal force, tension. Every single problem needs FBD first.
Friction
FBD shows direction of friction force — the most common mistake area in all of physics.
Work, Energy & Power
FBD identifies which forces do work. W = F·d·cosθ — FBD gives you the angle θ directly.
Circular Motion
Net inward force = centripetal force. FBD identifies which forces provide this centripetal force.
Electrostatics
Coulomb's force, charge in field, dipole. FBD shows direction of attraction and repulsion.
Moving Charges & Magnetism
Lorentz force on charges and current conductors. Right-hand rule + FBD = full solution.
Rotational Mechanics
Torque-based FBD. Draw forces at their exact point of application. τ = r × F.
FBD → Marks Pipeline
In board exams, drawing a correct FBD earns 1–2 marks even if the final answer is wrong. Examiners reward method over result.
Concept Building
The Golden Rule — Memorize This
"Draw ALL forces acting ON the object — NOT forces the object exerts ON others."
🔍 What is a Free Body Diagram?
A Free Body Diagram (FBD) is a simple, clean drawing where you take ONE object and isolate it completely. You then replace every connection to other objects with a force arrow. The result is a picture that shows exactly what forces act on your chosen object — and nothing else.
Normal force from surfaces
Tension from strings
Friction from rough surfaces
Applied forces
Forces the object exerts on others
Internal forces (for whole system)
Velocity arrows
Acceleration arrows
⚡ Internal vs External Forces
External forces appear in FBD. Internal forces cancel and do NOT appear in the FBD of the whole system.
System = both teams. External = ground friction. Internal = rope tension (cancels). For FBD of ONE person → rope tension becomes external!
🧲 Why Isolate the Body?
Physics can only analyze ONE object at a time with F = ma. Isolation ensures:
- Clear picture of all forces
- No confusion between action/reaction
- Clean equations that actually solve
- Full marks in board exams
| Force Name | Symbol | Direction | When It Acts | Formula |
|---|---|---|---|---|
| Weight / Gravity | W or mg | Always ↓ (downward) | Always, on every object with mass | mg (m×10) |
| Normal Force | N | ⊥ to surface, away from it | Object touching a surface | Varies |
| Tension | T | Along string, away from object | Connected by string/rope/cable | Varies |
| Friction | f | Opposite to motion/tendency | Object on rough surface | μN |
| Applied Force | F | As given in problem | Pushed or pulled externally | Given |
| Spring Force | F_s | Opposite to stretch/compress | Connected to spring | kx |
| Electric Force | F_E | Along E for +q; opposite for −q | Charged particle in electric field | qE |
| Magnetic Force | F_B | ⊥ to both velocity and B | Moving charge in magnetic field | qvB |
| Buoyancy | F_b | Always ↑ (upward) | Object submerged in fluid | ρVg |
The FBD Algorithm
Board Exam Mantra
"No FBD = No Marks." Follow these 7 steps every single time. No shortcuts.
Identify the Object
Choose which body you want to analyze. Circle it mentally. You can only analyze ONE body at a time (unless treating a combined system).
Isolate It (Mental Cut)
Imagine cutting all strings, surfaces, and connections. Draw the object alone in the center of your paper — just a simple box or dot.
Add Weight First (Always!)
Weight (mg) acts on EVERY object. Draw it downward first — before any other force. This is the one you most often forget.
Replace Surroundings with Forces
Everything you "cut" in Step 2 becomes a force arrow. Table removed → Normal force ↑. String removed → Tension. Ground removed → Normal force.
Draw All Forces with Direction
Draw each force as an arrow starting from the object's center. Arrow length can suggest relative magnitude — longer arrow = bigger force.
Label Every Force
Label every arrow: W or mg (weight), N (normal), T (tension), f (friction), F (applied). Add subscripts if needed: T₁, T₂, N₁, N₂.
Choose Axes & Write Equations
Choose x and y axes. For inclines, tilt axes along and perpendicular to incline. Resolve forces and write: ΣFx = max, ΣFy = may.
Visual Diagram Library
1. Block on Smooth Table
2 forces only. N balances mg perfectly. Object at rest → N = mg.
2. Block Hanging by String
String pulls UP with T. Gravity pulls DOWN with mg. T = mg at rest.
3. Object in Free Fall
ONLY gravity acts. No normal force (not on surface). a = g downward.
4. Block Pushed (Smooth Surface)
4 forces: N↑, mg↓, F→. No friction on smooth surface. F = ma.
5. Incline — No Friction
N perpendicular to incline = mgcosθ. Component along incline = mgsinθ causes acceleration.
6. Incline — With Friction
Block slides DOWN → friction acts UP incline. a = gsinθ − μgcosθ.
7. Block Pulled UP Incline
Moving UP → friction now acts DOWN the incline. F must overcome both mgsinθ AND friction.
8. Two Blocks on Incline
Connected blocks on incline move together. Same acceleration. Tension is internal to system.
9. Two Blocks — Horizontal
Draw FBD of EACH block separately. Tension T is external to each block individually.
10. Atwood Machine
Same tension T throughout (massless string, frictionless pulley). Draw each mass separately.
11. Table + Hanging Mass
Horizontal block pulled by hanging mass through pulley. Same acceleration for entire system.
12. Static Friction (Not Moving)
Static friction exactly equals applied force. f_s ≤ μ_s × N. Block stays still.
13. Limiting Friction
At limiting friction — block JUST about to move. Any more force → motion begins. f_max = μ_s N.
14. Kinetic Friction (Moving)
Kinetic friction f_k = μ_k × N. Note: μ_k is always less than μ_s!
15. Block Pressed Against Wall
Wall provides normal force horizontally. Friction acts upward to balance gravity.
16. Conical Pendulum
Resolve T into vertical (balances mg) and horizontal (centripetal) components.
17. Vertical Circle — Bottom
At bottom: T and mg oppose. Net upward = centripetal. T is MAXIMUM at the bottom.
18. Vertical Circle — Top
At top: BOTH T and mg point toward center (downward). T is minimum. Min speed: v = √(rg).
19. Banked Road (No Friction)
N tilted → horizontal Nsinθ provides centripetal force. Ncosθ balances mg.
20. Charge in Electric Field
Electric force F = qE. +q along E, −q against E. Add mg if particle has mass.
21. Two Charges — Coulomb Force
FBD of each charge separately. Each charge has a force ON it from the other charge.
22. Lorentz Force — Charge in B Field
Magnetic force ⊥ to velocity. Use right-hand rule: v along →, B out → F points up.
23. Current Wire in B Field
Force on current conductor F = BIL. Direction from Fleming's Left Hand Rule.
24. Elevator — Accelerating Up
N − mg = ma. N = m(g+a) > mg. Person feels heavier when elevator accelerates up.
25. Elevator — Accelerating Down
mg − N = ma. N = m(g−a) < mg. If a = g → N = 0 → weightlessness!
26. Block + Spring System
Spring force F = kx, opposite to compression/stretch. 4 forces total on the block.
27. Tension Varies in Rope
Top of rope supports more weight (rope below + block). T maximum at top, minimum at bottom.
Common Mistakes
❌ Missing Normal Force
Forgetting to draw N when block is on incline or any surface. N is perpendicular to the surface — not vertical on inclines!
❌ Wrong Friction Direction
Drawing friction in the direction of motion. Friction ALWAYS opposes motion or tendency of motion.
❌ Drawing "Force of Motion"
Adding an arrow in the direction of motion (velocity). There is NO "force of motion" — velocity is not a force!
❌ Confusing Action-Reaction
Including forces the object exerts ON others in the object's own FBD. Newton's 3rd law pairs NEVER appear in the same FBD.
❌ Not Resolving Forces on Incline
Using mg directly without resolving into components parallel and perpendicular to the incline surface.
❌ Normal Force Pointing Vertically on Incline
Drawing N vertically upward when block is on an incline. N is always PERPENDICULAR to the surface, not vertical!
❌ Forgetting to Isolate First
Drawing FBD of the whole setup and getting forces mixed up between different objects.
❌ Missing Tension in Connected Bodies
When two blocks are connected, tension must be drawn on EACH block separately as a force acting ON it.
5 Solved Examples
Board Exam Strategy
"Always draw FBD first." Convert diagram → equation → answer. Skipping the FBD skips the marks.
Problem: A 5 kg block on 30° incline. μk = 0.3. Block slides down. Find acceleration.
Step 1 — Draw FBD
Forces: (a) mg = 50 N ↓, (b) N perpendicular to incline, (c) Kinetic friction f up the incline
Step 2 — Tilt Axes Along Incline
x-axis: along incline (positive = down), y-axis: perpendicular to incline
Step 3 — Write Equations
Problem: m₁ = 3 kg, m₂ = 5 kg connected over a pulley. Find a and T.
Step 1 — FBD of each mass
m₁: T (up), m₁g (down) | m₂: T (up), m₂g (down). Since m₂ > m₁, m₂ goes down.
Step 2 — Apply Newton's Second Law
Step 3 — Solve the System
Problem: 60 kg person in elevator accelerating UP at 3 m/s². Find apparent weight.
Step 1 — FBD of Person
Forces: N (up from elevator floor), mg = 600 N (down). Net force upward = ma.
Step 2 — Apply F = ma
Bonus: If elevator accelerates DOWN at 3 m/s² → N = 60×7 = 420 N (feels only 42 kg!)
Problem: Conical pendulum L = 1 m, speed v = 2 m/s, mass m = 0.5 kg. Find θ and T.
Step 1 — FBD of Bob
Forces: T along string (upward + inward), mg = 5 N downward.
Step 2 — Resolve T into components
Step 3 — Divide equations (2)÷(1)
Problem: F = 30 N applied to block A (2 kg) connected to block B (3 kg) via string. Smooth surface. Find a and T.
Step 1 — FBD of Whole System (to find a)
Step 2 — FBD of Block B Alone (to find T)
Only horizontal force on B = Tension T (T pulls it forward)
Step 3 — Verify with Block A
Teaching Tricks & Hacks
"Imagine you're in a tug-of-war with 3 friends pulling you in different directions. Before you can figure out who wins, you need to know exactly how hard each person is pulling. A Free Body Diagram is exactly that — a picture that shows every force pulling on YOU, so we can calculate what happens. Nothing more, nothing less."
🧠 Memory Shortcuts
- W.A.N.T. = Weight, Applied, Normal, Tension (force checklist)
- "Friction always fights" = opposes whatever the object wants to do
- "N is always neat" = always ⊥ to the contact surface
- "mg goes down, always down" = no exceptions, ever
- "SIN goes along, COS goes cross" = mgsinθ along incline, mgcosθ perpendicular
- "Isolate before you calculate" = draw FBD before any equation
✋ Gesture-Based Teaching
- Pointing game: Point down = weight. Push up from below = normal. Pull string = tension.
- Body as block: Stand up. Someone pushes (F). Ground pushes your feet (N). Gravity pulls (mg). Friction stops you sliding.
- Book stack: 3 books stacked — pull middle one. Ask: what forces act on middle book ONLY?
- String + eraser: Hold string with eraser attached. When still: T = mg. Move up: feel T increase!
🖊️ Board Drawing Techniques
- Draw the OBJECT first (box/circle), then all arrows
- Use different colors: Red = weight, Green = normal, Blue = tension, Orange = friction
- Make arrows start from center of the object
- Write force name at arrowhead, not at tail
- For inclines, tilt your whole diagram — students find it much easier
- Mark balanced cases: equal length opposite arrows = equilibrium
🎯 Student Thinking Process
- Step 1: "Which object?" → Circle it mentally
- Step 2: "Touching anything?" → N for each surface
- Step 3: "Has mass?" → mg downward (always!)
- Step 4: "Any strings?" → T away from object
- Step 5: "Surface rough?" → Friction opposite motion
- Step 6: "Any other force?" → Add it
- Step 7: Write ΣF = ma equations!
📝 Exam Tips — Board & JEE
Show BOTH FBD AND equation for full marks
For inclines: always specify positive direction
1 mark for FBD + 2 marks for equation + 2 for answer
Spend 30 seconds on FBD first — always
For multi-body problems: draw SEPARATE FBD for each
Check: does number of unknowns = number of equations?
Rapid Revision Sheet
Weight (mg)
↓ Always downward
mg = mass × 10 m/s²
Acts on EVERY object
Never changes direction
Even on inclines!
Normal (N)
⊥ to surface always
Away from surface
Only when touching
N = 0 in free fall
N = mgcosθ on incline
Tension (T)
Along string
Away from object
Same T throughout
(massless string)
T ≥ 0 always
Friction (f)
Opposes motion
Static: f ≤ μ_s N
Kinetic: f = μ_k N
μ_k < μ_s always
On rough surfaces only
Incline Rules
N = mgcosθ
Along: mgsinθ
Tilt your axes!
Friction opposes slide
Resolve mg always
Elevator Cases
a↑: N = m(g+a)
a↓: N = m(g−a)
a = g down: N = 0
Constant v: N = mg
Weightlessness: a = g
Vertical Circle
Bottom: T−mg = mv²/r
Top: T+mg = mv²/r
T minimum at TOP
T maximum at BOTTOM
Min v = √(rg)
Class 12 Forces
Electric: F = qE
+q along E direction
−q opposite to E
Magnetic: F = qvB
Always ⊥ to velocity
Atwood Machine
a = (m₂−m₁)g/(m₁+m₂)
T = 2m₁m₂g/(m₁+m₂)
Same T for both
Same acceleration
m₂ > m₁ → m₂ falls
When to Use FBD
Any force question
Any incline problem
Any pulley/string
Any circular motion
Any field (E or B)
"Physics without FBD is like solving mathematics without writing steps — you might get the answer, but you'll never get the marks."— Master FBD. Master Physics. Master CBSE.